Digital imaging systems, including, for example, ink jet, electrophotographic and xerographic printing or rendering environments can include a number of intentional and unintentional periodicities in their rendering processes. For example, many raster output scanners (ROS) associated with electrophotographic and xerographic marking engines include a rotating polygonal mirror as part of a motor polygon assembly (MPA). One or more laser beams are reflected off of facets of the rotating mirror onto an imaging surface. Imperfections in the mirrors, alignment of the rotating mirror and facets, and the rate at which the mirror is rotated can affect the position, intensity and focus of the reflected beam with the periodicity of the mirror rotation. The cyclic nature of gears associated, for example, with moving an ink jet print head or with transporting print media, can also contribute periodicities to some rendering processes. Additionally, where print media is transported by or processed by rolls, roll run-out or imperfections in the shape or alignment of the rolls can contribute periodic variations in the rendering process. For instance, roll run-out imperfections may create variation to development pressure and/or in-media transportation speed. Furthermore, subtle accelerations and decelerations are associated with points in time of positive gear-tooth engagement and disengagement (or backlash).
In the best of situations, these periodic excitations due to problematic rendering processes occur at frequencies that are high enough to be imperceptible by the human vision system. However, even excitations that are themselves at an imperceptively high frequency can combine or beat with other imaging periodicities to produce perceptible banding or moiré artifacts in a rendered image. For example, problematic rendering excitations can combine with fundamental, harmonic and beat frequencies associated with halftone screens used in the rendering process.
In monochrome or black and white rendering applications, where only one halftone screen is used, it is fairly simple to select a halftone screen that does not include periodicities (i.e., fundamental, harmonic and beat frequencies) in the same direction or at the same angle as one or more known problematic excitations. However, in color rendering, where two or more halftone screens are used (one for each separation), it is difficult to find a set of halftone screens that avoid including periodicities (i.e., fundamentals, harmonics and beats) in the same direction or angle of a problematic excitation.
In fact, a great deal of effort has been spent to solve the lesser problem of finding sets of halftone screens for rendering color that do not produce objectionable moiré due to beats between frequency components of the screens themselves. For example, see Spectral Analysis and Minimization of Moire Patterns in Color Separation by Amidror, Hersch and Ostromoukhov in the Journal of Electronic Imaging, Vol. 3, no. 3, pages 295-317 (July 1994); U.S. Pat. No. 5,381,247 to Hains for a Method for Reducing Two-Color Moire in Four-Color printing, which issued Jan. 10, 1995; U.S. Pat. No. 4,537,470 to Schoppmeyer for Screen Systems for Multicolor Printing, which issued Aug. 27, 1985; and U.S. Pat. No. 6,798,539 B1 to Wang, et al. for a method for moire-free color halftoning using non-orthogonal cluster screens, which issued Sep. 28, 2004.
Halftone banding has been a long standing problem for digital printers, and it can be one of the most serious image quality problems. Banding can be placed into two categories. One type of banding is due to the excitation frequency from the mechanical or opto-mechanical being directly observable as a spatial frequency on the final print. A second type of banding is due to halftone periodic structure beating with a machine excitation frequency to produce a new frequency that is observed on a print. For example, a beat may occur between a frequency component of a halftone screen or combination of halftone screens and a harmonic of a ROS MPA once-around frequency.
Periodic excitations from the marking process are typically periodic in the process direction. However, periodic excitations can also exist in the cross-process direction and can occur from a variety of sources, such as segmented photoreceptor charging devices or segmentation imaging devices such as an LED image bar array. Regarding process direction excitations, in past studies, it has been determined that lowering the amplitude of beat-type banding sometimes can be accomplished by rotating a halftone screen so that its harmonics are a small amount off of the 90° axis, i.e., process-direction. For example, 2° has worked for some screens and a monochrome screen with this property has been used in previous printers and patent application publication No. 2006/0232822 discloses this principle applied to process-color screen sets. Notably, it has been discovered that small angle rotations do not always reduce banding amplitude, and it is difficult to find screen geometries that have this slight rotation.
For the beat-based banding case, it has been discovered that using a screen set with a nonrotated (0°/90° fundamental frequencies) screen can solve beat-based banding in some printing systems. One disadvantage associated with this approach is customer dissatisfaction with a screen being at 0°/90°. Notably, low raster resolution (600 spi) printers have not been able to produce a screen set that solves the problem without using a 0°/90° screen or more complicated supercell designs.